SOLUTION: fiza is 3 years older than half of her mother's age. The sum of their current ages is 75. How old will fiza be in 10 years?

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Question 891055: fiza is 3 years older than half of her mother's age. The sum of their current ages is 75. How old will fiza be in 10 years?
Found 2 solutions by josgarithmetic, MathTherapy:
Answer by josgarithmetic(39621) About Me  (Show Source):
You can put this solution on YOUR website!
Questions 891055 and 891056 are the same problem as different examples.

nameOne is k years older than nameTwo. In c years, the sume of their ages will be T. How old
is each now?

Let x = age of nameOne
Let y = age of nameTwo

x=y%2Bk; and %28x%2Bc%29%2B%28y%2Bc%29=T.
Solve for x and y.

x-y=k and x%2By%2B2c=T,
x%2By=T-2c
-
You can use Elimination Method to begin handling the system:
------------------
x-y=k
-
x%2By=T-2c
------------------
Simply adding the corresponding members,
2x=T%2Bk-2c
highlight%28x=%28T%2Bk%29%2F2-c%29
-
The first equation may be simplest for now getting a formula for y.
y=x-k
y=%28T%2Bk%29%2F2-c-k
y=T%2F2%2Bk%2F2-k-c
y=T%2F2-k%2F2-c
highlight%28y=%28T-k%29%2F2-c%29
-
-
Now just substitute the corresponding values from the original description for T, k, and c.

Answer by MathTherapy(10555) About Me  (Show Source):
You can put this solution on YOUR website!

fiza is 3 years older than half of her mother's age. The sum of their current ages is 75. How old will fiza be in 10 years?


Let Fiza's and Mom's current ages be F and M, respectively

Then, F+=+%281%2F2%29M+%2B+3____F+=+M%2F2+%2B+3____2F = M + 6____M = 2F - 6 ----- eq (i)

Also, M + F = 75 ------ eq (ii)

2F - 6 + F = 75 ------- Substituting 2F - 6 for M in eq (ii)

2F + F = 75 + 6

3F = 81

F, or Fiza's current age = 81%2F3, or 27

In 10 years' time, Fiza will be 27 + 10, or highlight_green%2837%29 years-old



You can do the check!! 



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